I have a feeling that the "image" you're trying to "restore from" isn't a good one.
Here's something to try.
It may not work. Won't make any promises.
But I suggest that you try it anyway.
You'll need a USB flash drive.
It should be 32gb, but I think you might be able to get by with 16gb.
8gb won't work.
(This might also work with a USB external hard drive, but you'll lose whatever was on the drive -- don't do this unless you don't mind erasing the drive!)
Get to the utilities menu you talked about before.
Then, plug in the flashdrive.
Open Disk Utility.
Can DU "see" the flash drive?
If so, ERASE IT to "Mac OS extended with journaling enabled".
Now, quit Disk Utility and see if you can open the OS installer.
If it opens, "aim it" at the flashdrive
See if the installer will install a copy of the OS ONTO THE FLASHDRIVE (and NOT onto the internal drive).
Does this work?
If it does, the installer will close and you should see a brand-new Mac setup screen.
Go ahead and set up a basic account with the username and password of your choice.
See if you can "get it to the finder".
IF you can get this far...
In the finder, can you see the internal hard drive on the desktop?
You may have to go to "finder preferences" and in the "general" tab click the checkbox to show the hard drive on the desktop.
Can you get this far?
WHY I'm asking you to do this:
IF the internal drive has a problem, you need a way to "boot the Mac externally".
That's why we created a fully-bootable-to-the-finder copy of the OS on a flash drive.
The idea is to get the iMac "up and running" again, any way possible.